Analysis of high-resolution electron diffraction patterns from purple membrane labelled with heavy-atoms

Progress in the structure determination of bacteriorhodopsin, the protein component of purple membrane from Halobacterium halobium has been limited by the lack of three-dimensional phase information between 6 and 3 A resolution. By analogy with X-ray methods, it is possible that heavy-atom labelling of the membrane crystal may provide heavy-atom derivatives that can be used for phasing by the multiple isomorphous replacement method. This paper describes the screening of heavy-atom compounds as potential derivatives, and the evaluation of the data collected from these heavy-atom-labelled membranes. Improvements in the methods for collecting electron diffraction data and analysing and merging the data are presented. Diffraction patterns of purple membrane samples were taken at -120 degrees C to minimize radiation damage. About 30 heavy-atom compounds were tested for use as potential derivatives. The diffraction patterns from labelled membranes were analysed by examining 6.5 A difference Fourier maps. Two heavy-atom compounds were selected for three-dimensional data collection at 3 A resolution. In addition, a full set of native data at -120 degrees C was collected to 2.7 A resolution. The intensity merging, heavy-atom derivative evaluation, heavy-atom refinement and the calculation of phases are presented. Phases are compared to those determined by electron microscope imaging, and limitations of the method are discussed. It is concluded that, with the present accuracy of data collection and the present magnitude of delta F/F available for the derivatives, the phasing power is too small. The phases that are obtained are not sufficiently accurate to provide a reliably interpretable map. It may be possible, however, to use the heavy-atom derivative data in difference Fourier calculations in which the presence of a peak would confirm the phases calculated from a model or obtained by electron microscope imaging.     

3D parallel coordinate systems--a new data visualization method in the context of microscopy-based multicolor tissue cytometry.

BACKGROUND: Presentation of multiple interactions is of vital importance in the new field of cytomics. Quantitative analysis of multi- and polychromatic stained cells in tissue will serve as a basis for medical diagnosis and prediction of disease in forthcoming years. A major problem associated with huge interdependent data sets is visualization. Therefore, alternative and easy-to-handle strategies for data visualization as well as data meta-evaluation (population analysis, cross-correlation, co-expression analysis) were developed. METHODS: To facilitate human comprehension of complex data, 3D parallel coordinate systems have been developed and used in automated microscopy-based multicolor tissue cytometry (MMTC). Frozen sections of human skin were stained using the combination anti-CD45-PE, anti-CD14-APC, and SytoxGreen as well as the appropriate single and double negative controls. Stained sections were analyzed using automated confocal laser microscopy and semiquantitative MMTC-analysis with TissueQuest 2.0. The 3D parallel coordinate plots are generated from semiquantitative immunofluorescent data of single cells. The 2D and 3D parallel coordinate plots were produced by further processing using the Matlab environment (Mathworks, USA). RESULTS: Current techniques in data visualization primarily utilize scattergrams, where two parameters are plotted against each other on linear or logarithmic scales. However, data evaluation on cartesian x/y-scattergrams is, in general, only of limited value in multiparameter analysis. Dot plots suffer from serious problems, and in particular, do not meet the requirements of polychromatic high-context tissue cytometry of millions of cells. The 3D parallel coordinate plot replaces the vast amount of scattergrams that are usually needed for the cross-correlation analysis. As a result, the scientist is able to perform the data meta-evaluation by using one single plot. On the basis of 2D parallel coordinate systems, a density isosurface is created for representing the event population in an intuitive way. CONCLUSIONS: The proposed method opens new possibilities to represent and explore multidimensional data in the perspective of cytomics and other life sciences, e.g., DNA chip array technology. Current protocols in immunofluorescence permit simultaneous staining of up to 17 markers. Showing the cross-correlation between these markers requires 136 scattergrams, which is a prohibitively high number. The improved data visualization method allows the observation of such complex patterns in only one 3D plot and could take advantage of the latest developments in 3D imaging.     

A statistical model of ChIA-PET data for accurate detection of chromatin 3D interactions

Identification of three-dimensional (3D) interactions between regulatory elements across the genome is crucial to unravel the complex regulatory machinery that orchestrates proliferation and differentiation of cells. ChIA-PET is a novel method to identify such interactions, where physical contacts between regions bound by a specific protein are quantified using next-generation sequencing. However, determining the significance of the observed interaction frequencies in such datasets is challenging, and few methods have been proposed. Despite the fact that regions that are close in linear genomic distance have a much higher tendency to interact by chance, no methods to date are capable of taking such dependency into account. Here, we propose a statistical model taking into account the genomic distance relationship, as well as the general propensity of anchors to be involved in contacts overall. Using both real and simulated data, we show that the previously proposed statistical test, based on Fisher''s exact test, leads to invalid results when data are dependent on genomic distance. We also evaluate our method on previously validated cell-line specific and constitutive 3D interactions, and show that relevant interactions are significant, while avoiding over-estimating the significance of short nearby interactions.     

Automated three-dimensional detection and shape classification of dendritic spines from fluorescence microscopy images

A fundamental challenge in understanding how dendritic spine morphology controls learning and memory has been quantifying three-dimensional (3D) spine shapes with sufficient precision to distinguish morphologic types, and sufficient throughput for robust statistical analysis. The necessity to analyze large volumetric data sets accurately, efficiently, and in true 3D has been a major bottleneck in deriving reliable relationships between altered neuronal function and changes in spine morphology. We introduce a novel system for automated detection, shape analysis and classification of dendritic spines from laser scanning microscopy (LSM) images that directly addresses these limitations. The system is more accurate, and at least an order of magnitude faster, than existing technologies. By operating fully in 3D the algorithm resolves spines that are undetectable with standard two-dimensional (2D) tools. Adaptive local thresholding, voxel clustering and Rayburst Sampling generate a profile of diameter estimates used to classify spines into morphologic types, while minimizing optical smear and quantization artifacts. The technique opens new horizons on the objective evaluation of spine changes with synaptic plasticity, normal development and aging, and with neurodegenerative disorders that impair cognitive function.     

Predicting germination response to temperature. II. Three-dimensional regression, statistical gridding and iterative-probit optimization using measured and interpolated-subpopulation data

BACKGROUND AND AIMS: Most current thermal-germination models are parameterized with subpopulation-specific rate data, interpolated from cumulative-germination-response curves. The purpose of this study was to evaluate the relative accuracy of three-dimensional models for predicting cumulative germination response to temperature. Three-dimensional models are relatively more efficient to implement than two-dimensional models and can be parameterized directly with measured data. METHODS: Seeds of four rangeland grass species were germinated over the constant-temperature range of 3 to 38 degrees C and monitored for subpopulation variability in germination-rate response. Models for estimating subpopulation germination rate were generated as a function of temperature using three-dimensional regression, statistical gridding and iterative-probit optimization using both measured and interpolated-subpopulation data as model inputs. KEY RESULTS: Statistical gridding is more accurate than three-dimensional regression and iterative-probit optimization for modelling germination rate and germination time as a function of temperature and subpopulation. Optimization of the iterative-probit model lowers base-temperature estimates, relative to two-dimensional cardinal-temperature models, and results in an inability to resolve optimal-temperature coefficients as a function of subpopulation. Residual model error for the three-dimensional model was extremely high when parameterized with measured-subpopulation data. Use of measured data for model evaluation provided a more realistic estimate of predictive error than did evaluation of the larger set of interpolated-subpopulation data. CONCLUSIONS: Statistical-gridding techniques may provide a relatively efficient method for estimating germination response in situations where the primary objective is to estimate germination time. This methodology allows for direct use of germination data for model parameterization and automates the significant computational requirements of a two-dimensional piece-wise-linear model, previously shown to produce the most accurate estimates of germination time.     

Low-resolution density maps from atomic models: how stepping "back" can be a step "forward"

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15-40 A), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

基于CVM的海涂湿地生态服务价值的模糊评估模型

正确评估海涂湿地生态服务价值有助于加强人们保护海涂湿地的意识,为海涂湿地围垦生态补偿标准的制定提供依据。视价格"便宜"、"适中"和"昂贵"为模糊集,基于CVM法区间型数据建立了传统模糊统计模型、赋权模糊统计模型和三相划分模型,并以此评价了杭州湾国家湿地公园单位面积年生态系统服务价值。结果显示:3种方法得到的单价分别为10.28、10.38、9.76元m~(-2)a~(-1),三者一致程度较高,与国内沿海湿地价值比较接近。分析了"生态价值"概念客观上的"模糊性"引致模糊数学模型的合理性;采用"橄榄球"式赋权建立赋权模糊统计模型以克服传统模糊统计模型中对区间数据均匀赋权的不合理性,结果在隶属度函数的光滑性和拟合度上好于后者;第三,三相划分模型拟合出3个模糊集的隶属度函数,可以比较相同价格在不同模糊集中隶属度差异。建立的模型对于基于CVM法的生态资源价值评估具有借鉴意义。     

Graph-theoretical assignment of secondary structure in multidimensional protein NMR spectra: Application to the lac repressor headpiece

Summary A novel procedure is presented for the automatic identification of secondary structures in proteins from their corresponding NOE data. The method uses a branch of mathematics known as graph theory to identify prescribed NOE connectivity patterns characteristic of the regular secondary structures. Resonance assignment is achieved by connecting these patterns of secondary structure together, thereby matching the connected spin systems to specific segments of the protein sequence. The method known as SERENDIPITY refers to a set of routines developed in a modular fashion, where each program has one or several well-defined tasks. NOE templates for several secondary structure motifs have been developed and the method has been successfully applied to data obtained from NOESY-type spectra. The present report describes the application of the SERENDIPITY protocol to a 3D NOESY-HMQC spectrum of the ¹⁵N-labelled lac repressor headpiece protein. The application demonstrates that, under favourable conditions, fully automated identification of secondary structures and semi-automated assignment are feasible.Abbreviations 2D, 3D two-, three-dimensional - NOESY nuclear Overhauser enhancement spectroscopy - HMQC heteronuclear multiple quantum coherence - SSE secondary structure element - SERENDIPITY SEcondary structuRE ideNtification in multiDImensional ProteIn specTra analYsis Supplementary Material available from the authors: Two tables containing the total number of mappings resulting from the graph search procedure for simulated and experimental NOE data.     

Three‐dimensional static optical coherence elastography based on inverse compositional Gauss‐Newton digital volume correlation

The three‐dimensional (3D) mechanical properties characterization of tissue is essential for physiological and pathological studies, as biological tissue is mostly heterogeneous and anisotropic. A digital volume correlation (DVC)‐based 3D optical coherence elastography (OCE) method is developed to measure the 3D displacement and strain tensors. The DVC algorithm includes a zero‐mean normalized cross‐correlation criterion‐based coarse search regime, an inverse compositional Gauss‐Newton fine search algorithm and a local ternary quadratic polynomial fitting strain calculation method. A 3D optical coherence tomography (OCT) scanning protocol is proposed through theoretical analysis and experimental verification. Measurement errors of the DVC‐based 3D OCE method are evaluated to be less than 2.0 μm for displacements and 0.30% for strains by rigid body motion experiments. The 3D displacements and strains of a phantom and a specimen of chicken breast tissue under compression are measured. Results of the phantom show a good agreement with theoretical analysis and tensile testing. The strains of the chicken breast tissue indicate anisotropic biomechanical properties. This study provides an effective method for 3D biomechanical property studies of soft tissue and improves the development of 3D OCE techniques.     

GPU-Accelerated Framework for Intracoronary Optical Coherence Tomography Imaging at the Push of a Button

Frequency domain optical coherence tomography (FD-OCT) has become one of the important clinical tools for intracoronary imaging to diagnose and monitor coronary artery disease, which has been one of the leading causes of death. To help more accurate diagnosis and monitoring of the disease, many researchers have recently worked on visualization of various coronary microscopic features including stent struts by constructing three-dimensional (3D) volumetric rendering from series of cross-sectional intracoronary FD-OCT images. In this paper, we present the first, to our knowledge, "push-of-a-button" graphics processing unit (GPU)-accelerated framework for intracoronary OCT imaging. Our framework visualizes 3D microstructures of the vessel wall with stent struts from raw binary OCT data acquired by the system digitizer as one seamless process. The framework reports the state-of-the-art performance; from raw OCT data, it takes 4.7 seconds to provide 3D visualization of a 5-cm-long coronary artery (of size 1600 samples x 1024 A-lines x 260 frames) with stent struts and detection of malapposition automatically at the single push of a button.     

A new multiscale micromechanical model of vertebral trabecular bones

A new three-dimensional (3D) multiscale micromechanical model has been suggested as adept at predicting the overall linear anisotropic mechanical properties of a vertebral trabecular bone (VTB) highly porous microstructure. A nested 3D modeling analysis framework spanning the multiscale nature of the VTB is presented herein. This hierarchical analysis framework employs the following micromechanical methods: the 3D parametric high-fidelity generalized method of cells (HFGMC) as well as the 3D sublaminate model. At the nanoscale level, the 3D HFGMC method is applied to obtain the effective elastic properties of a representative unit cell (RUC) representing the mineral collagen fibrils composite. Next at the submicron scale level, the 3D sublaminate model is used to generate the effective elastic properties of a repeated stack of multilayered lamellae demonstrating the nature of the trabeculae (bone-wall). Thirdly, at the micron scale level, the 3D HFGMC method is used again on a RUC of the highly porous VTB microstructure. The VTB-RUC geometries are taken from microcomputed tomography scans of VTB samples harvested from different vertebrae of human cadavers \((n=10)\). The predicted anisotropic overall elastic properties for native VTBs are, then, examined as a function of age and sex. The predicted results of the VTBs longitudinal Young’s modulus are compared to reported values found in the literature. The proposed 3D nested modeling analysis framework provides a good agreement with reported values of Young’s modulus of single trabeculae as well as for VTB-RUC in the literature.     

Fast and accurate three-dimensional reconstruction from projections with random orientations via radon transforms

A new algorithm for three-dimensional reconstruction from randomly oriented projections has been developed. The algorithm recovers the 3D Radon transform from the 2D Radon transforms (sinograms) of the projections. The structure in direct space is obtained by an inversion of the 3D Radon transform. The mathematical properties of the Radon transform are exploited to design a special filter that can be used to correct inconsistencies in a data set and to fill the gaps in the Radon transform that originate from missing projections. Several versions of the algorithm have been implemented, with and without a filter and with different interpolation methods for merging the sinograms into the 3D Radon transform. The algorithms have been tested on analytical phantoms and experimental data and have been compared with a weighted back projection algorithm (WBP). A quantitative analysis of phantoms reconstructed from noise-free and noise-corrupted projections shows that the new algorithms are more accurate than WBP when the number of projections is small. Experimental structures obtained by the new methods are strictly comparable to those obtained by WBP. Moreover, the algorithm is more than 10 times faster than WPB when applied to a data set of 1000-5000 projections. Copyright 1999 Academic Press.     

Statistical evaluation of colocalization patterns in immunogold labeling experiments

The ultrastructural localization of various antigens in a cell using antibodies conjugated to gold particles is a powerful instrument in biological research. However, statistical or stereological tools for testing the observed patterns for significant clustering or colocalization are missing. The paper presents a method for the quantitative analysis of single or multiple immunogold labeling patterns using interpoint distances and tests the method using experimental data. The clustering or colocalization of gold particles was detected using various characteristics of the distribution of distances between them. Pair correlation and cross-correlation functions were used for exploratory analysis; second order reduced K (or cross-K) functions were used for testing the statistical significance of observed events. Confidence intervals of function values were estimated by Monte Carlo simulations of the Poisson process for independent particles, and results were visualized in histograms. Furthermore, a suitability of K functions modified by censoring or weighting was tested. The reliability of the method was assessed by evaluating the labeling patterns of nascent DNA and several nuclear proteins with known functions in replication foci of HeLa cells. The results demonstrate that the method is a powerful tool in biological investigations for testing the statistical significance of observed clustering or colocalization patterns in immunogold labeling experiments.     

Low-Resolution Density Maps from Atomic Models: How Stepping “Back” Can Be a Step “Forward”

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15–40 Å), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

A fully automatic 3D reconstruction method using simulated annealing enables accurate posterioric angular assignment of protein projections

Single-particle analysis is a structure determining method using electron microscopic (EM) images, which does not require protein crystal. In this method, projections are picked up and used to reconstruct a three-dimensional (3D) structure. When the conical tilting method is not available, the particle images are usually classified and averaged to improve the signal-to-noise ratio. The Euler angles of these average images must be posteriorically assigned to create a primary 3D model. We developed a new, fully automatic unsupervised Euler angle assignment method, which does not require an initial 3D reference and which is applicable to asymmetric molecules. In this method, the Euler angle of each average image is initially set randomly and then automatically corrected in relation to those of the other averages by iterated optimizations using the Simulated Annealing (SA) algorithm. At each iteration, the 3D structure is reconstructed based on the current Euler angles and reprojected back in the average-input directions. A modified cross-correlation between each reprojection and its corresponding original average is then calculated. The correlations are summed as a total 3D echo-correlation score to evaluate the Euler angles at this iteration. Then, one of the projections is selected, its Euler angle is changed randomly, and the score is also calculated. Based on the score change, judgment of whether to accept or reject the new angle is made using the SA algorithm, which is introduced to overcome the local minimums. After a certain number of iterations of this process, the angles of all averages converge so as to create a reliable primary 3D model. This echo-correlated 3D reconstruction with simulated annealing also has potential for wide application to general 3D reconstruction from various types of 2D images.     

PPiClust: efficient clustering of 3D protein-protein interaction interfaces

The biological mechanisms through which proteins interact with one another are best revealed by studying the structural interfaces between interacting proteins. Protein-protein interfaces can be extracted from three-dimensional (3D) structural data of protein complexes and then clustered to derive biological insights. However, conventional protein interface clustering methods lack computational scalability and statistical support. In this work, we present a new method named "PPiClust" to systematically encode, cluster, and analyze similar 3D interface patterns in protein complexes efficiently. Experimental results showed that our method is effective in discovering visually consistent and statistically significant clusters of interfaces, and at the same time sufficiently time-efficient to be performed on a single computer. The interface clusters are also useful for uncovering the structural basis of protein interactions. Analysis of the resulting interface clusters revealed groups of structurally diverse proteins having similar interface patterns. We also found, in some of the interface clusters, the presence of well-known linear binding motifs which were noncontiguous in the primary sequences. These results suggest that PPiClust can discover not only statistically significant, but also biologically significant, protein interface clusters from protein complex structural data.     

Modeling cell apoptosis for simulating three-dimensional multicellular morphogenesis based on a reversible network reconnection framework

Morphogenesis in multicellular organisms is accompanied by apoptotic cell behaviors: cell shrinkage and cell disappearance. The mechanical effects of these behaviors are spatiotemporally regulated within multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze 3D multicellular dynamics, 3D vertex models have been suggested, in which a reversible network reconnection (RNR) model has successfully expressed 3D cell rearrangements during large deformations. To analyze the effects of apoptotic cell behaviors on 3D multicellular morphogenesis, we modeled cell apoptosis based on the RNR model framework. Cell shrinkage was modeled by the potential energy as a function of individual cell times during the apoptotic phase. Cell disappearance was modeled by merging neighboring polyhedrons at their boundary surface according to the topological rules of the RNR model. To establish that the apoptotic cell behaviors could be expressed as modeled, we simulated morphogenesis driven by cell apoptosis in two types of tissue topology: 3D monolayer cell sheet and 3D compacted cell aggregate. In both types of tissue topology, the numerical simulations successfully illustrated that cell aggregates gradually shrank because of successive cell apoptosis. During tissue shrinkage, the number of cells in aggregates decreased while maintaining individual cell size and shape. Moreover, in case of localizing apoptotic cells within a part of the 3D monolayer cell aggregate, the cell apoptosis caused the global tissue bending by pulling on surrounding cells. In case of localizing apoptotic cells on the surface of the 3D compacted cell aggregate, the cell apoptosis caused successive, directional cell rearrangements from the inside to the surface. Thus, the proposed model successfully provided a basis for expressing apoptotic cell behaviors during 3D multicellular morphogenesis based on an RNR model framework.     

Visualizing the Indefinable: Three-Dimensional Complexity of ‘Infectious Diseases’

Background

The words ‘infection’ and ‘inflammation’ lack specific definitions. Here, such words are not defined. Instead, the ability to visualize host-microbial interactions was explored.

Methods

Leukocyte differential counts and four bacterial species (Staphylococcus aureus, Streptococcus dysgalactiae, Staphylococcus chromogenes, and Escherichia coli) were determined or isolated in a cross-sectional and randomized study conducted with 611 bovine milk samples. Two paradigms were evaluated: (i) the classic one, which measures non-structured (count or percent) data; and (ii) a method that, using complex data structures, detects and differentiates three-dimensional (3D) interactions among lymphocytes (L), macrophages (M), and neutrophils (N).

Results

Classic analyses failed to differentiate bacterial-positive (B+) from –negative (B−) observations: B− and B+ data overlapped, even when statistical significance was achieved. In contrast, the alternative approach showed distinct patterns, such as perpendicular data inflections, which discriminated microbial-negative/mononuclear cell-predominating (MCP) from microbial-positive/phagocyte-predominating (PP) subsets. Two PP subcategories were distinguished, as well as PP/culture-negative (false-negative) and MCP/culture-positive (false-positive) observations. In 3D space, MCP and PP subsets were perpendicular to one another, displaying ≥91% specificity or sensitivity. Findings supported five inferences: (i) disease is not always ruled out by negative bacterial tests; (ii) low total cell counts can coexist with high phagocyte percents; (iii) neither positive bacterial isolation nor high cell counts always coincide with PP profiles; (iv) statistical significance is not synonymous with discrimination; and (v) hidden relationships cannot be detected when simple (non-structured) data formats are used and statistical analyses are performed before data subsets are identified, but can be uncovered when complexity is investigated.

Conclusions

Pattern recognition-based assessments can detect host-microbial interactions usually unobserved. Such cutoff-free, confidence interval-free, gold standard-free approaches provide interpretable information on complex entities, such as ‘infection’ and ‘inflammation’, even without definitions. To investigate disease dynamics, combinations of observational and experimental longitudinal studies, on human and non-human infections, are recommended.